Metric.hausdorffEDist_zero_iff_closure_eq_closure

∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α}, Metric.hausdorffEDist s t = 0 ↔ closure s = closure t

Two sets are at zero Hausdorff edistance if and only if they have the same closure.

Defined in: Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by: 3 results in Mathlib
Foundations: Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoEMetricSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.